Wordorigins.org

Ale and beer are both words that go back to Old English. Today, we distinguish the two as different beverages, but this distinction did not exist in Old English. Rather, ale was the commonly used word and beer was much rarer, being reserved for poetic language. But even in poetry its use was rare. Chaucer did not use the word, nor did William Langland in his Piers Ploughman.

Of the two words, ale is attested to slightly earlier. It appears c.940 in a manuscript called Læce Boc (Leech Book) in a recipe for an emetic, collected in Oswald Cockayne’s Leechdoms, Wortcunning, and Starcraft of Early England, Vol. II, 1865::

Do healfne bollan ealoð to [...] and gehæte þæt ealu.
(Add a half bowl of ale [...] and heat the ale.)

The word beer appears c.1000 in a translation of the Gospel of Luke:

He ne drincð win ne béor
(He drinks neither wine nor beer)

In the 15th century, brewers began adding hops to their product and by the 16th century, the word beer was being applied to this new style of brew. The modern distinction between ale and beer arose and the word beer became much more commonly used.

(Source: Oxford English Dictionary, 2nd Edition)